Speed and velocity

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Speed and velocity

Speed is a scalar quantity and can be an average or instantaneous value.

For example - If you drove to Vancouver (approximately 400 km away) in 4 hours your average speed would be 100km/hr. But at any given time your instantaneous speed could be more or less than 100 km/hr.

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Equations

v = d , where d = change in position (distance)

t t = time interval

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Example 1

A family travels for 60 miles at 20 miles per hour on a dirt road, and then travels another 60 miles at 60 mph on the pavement in order to get home from a camping trip. What is the average speed for the entire trip?

Plan:

What do we need to know?

What do we need to find first?

Would drawing it out help?

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To complete this…

We must find the total time taken and the distance travelled for each part of the journey first, then apply the equation.

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Example 2

A person travels for two hours at 30 miles per hour on horseback and then travels for one hour at 15 mph. What is the person’s average speed?

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Average velocity

Average velocity is calculated in the same manner as average speed only instead of distance we use the displacement (a vector).

average velocity is a vector quantity which means the answer must have a direction associated with it.

v = d , where d = change in position (displacement)

t t = time interval

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Example 3

A car moves due east at 30 km/h for 45 min, turns around, and moves due west at 40 km/h for 60 minutes. What is the average velocity for the entire trip?

Plan:

in this case it is important to draw out what the car is doing in order to find the total displacement, since it moves in opposite direction.

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from the example:

initially: 30 km/h for 45 minutes east. Find displacement 22.5 km[E]

then: 40 km/h for 60 minutes west. Find displacement

40 km [W]

Example 3 … the plan

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Vector additions

When vector diagrams are used, the vectors (arrows) are placed tip to tail.